The signing comes as reports indicated Lions free agent Jamaal Williams is engaged with other teams, including the Buffalo Bills and Cincinnati Bengals, after widely being expected to return to Detroit.
ESPN reported Montgomery, 25, will receive $11 million guaranteed as part of the deal.
A third-round pick in 2019, Montgomery has 3,609 rushing yards and 26 touchdowns over the last four seasons.
Chicago could turn to the draft to restock at the position, and top prospect Bijan Robinson (Texas) is projected to be a top-15 pick. The Bears pick at No. 9 following a trade with the Carolina Panthers.